Volterra-Type Discrete Integral Equations and Spectra of Non-self-adjoint Jacobi Operators

Stability criteria for the 2D α-Euler equations

“…A computation using (µ ± ) 2 + λµ ± − 1 = 0 shows that z ± n from (2.2) satisfy (1.1), see [24] for a similar compuation. In what follows we will need solutions z ± n to (2.2) only for ±n ≥ 0 but since solutions of (2.2) solve (1.1), they can be propagated to be defined for all n ∈ Z.…”

Perturbation determinants and discrete spectra of semi-infinite non-self-adjoint Jacobi operators

“…It has been proved recently in [12], that this bound can be refined. Actually, (0.7) holds for two-sided Jacobi operators as well.…”

“…Our strategy is similar to that in [8,12]. The key issue is the bound for the perturbation determinant…”

“…We study the Jost solutions by reducing the difference equation (0.4) to a Volterratype discrete integral equation, the standard idea in analysis, see, e.g., [20,Section 7.5] and [8,12]. The bounds for the Jost solutions stem from the successive approximations method.…”